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X और Y स्वतंत्र सामान्य चर हैं जिनका माध्य क्रमशः 50 और 80 है और मानक विचलन क्रमशः 4 और 3 है। X + Y का बंटन क्या है?

This question was previously asked in
SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. N(130, 7)
  2. N(130, 3)
  3. N(130, 5)
  4. N(130, 4)

Answer (Detailed Solution Below)

Option 3 : N(130, 5)
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Detailed Solution

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दिया गया है:

X और Y स्वतंत्र सामान्य चर हैं जिनके

माध्य (X) = 50

माध्य (Y) = 80

SD (σx) = 4

SD(σy) = 3

अवधारणा:

सामान्य बंटन N(μ, √(σ2x+ σ22)) द्वारा दर्शाया जाता है

गणना

चूंकि X और Y स्वतंत्र हैं तो

⇒ Z = X + Y ~ N(X + Y, (σ2x + σ2y)

⇒ P(Z) = P(X + Y)  ~ N(130, (42 + 32)

⇒ N(130, 25)

∴ N(μ, √(σ2x+ σ22), N(130, 5) है।

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